DETERMINATION OF ACOUSTIC RADIATION EFFICIENCY VIA ...

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Theses and Dissertations--Mechanical Engineering Mechanical Engineering

2019

DETERMINATION OF ACOUSTIC RADIATION EFFICIENCY VIA DETERMINATION OF ACOUSTIC RADIATION EFFICIENCY VIA

PARTICLE VELOCITY SENSOR WITH APPLICATIONS PARTICLE VELOCITY SENSOR WITH APPLICATIONS

Steven Conner Campbell University of Kentucky, [email protected] Digital Object Identifier: https://doi.org/10.13023/etd.2019.119

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The document mentioned above has been reviewed and accepted by the student’s advisor, on

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Steven Conner Campbell, Student

Dr. David W. Herrin, Major Professor

Dr. Alexandre Martin, Director of Graduate Studies

DETERMINATION OF ACOUSTIC RADIATION EFFICIENCY VIA PARTICLE

VELOCITY SENSOR WITH APPLICATIONS

_______________________________

THESIS

______________________________

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science

in Mechanical Engineering in the College of Engineering at the University of Kentucky

By

Steven Conner Campbell

Lexington, Kentucky

Director: Dr. David W. Herrin, Professor of Mechanical Engineering

Lexington, Kentucky

2019

Copyright © Steven Conner Campbell 2019

ABSTRACT OF THESIS



Acoustic radiation efficiency is defined as the ratio of sound power radiated to the surface vibration power of a piston with equivalent surface area. It has been shown that the radiation efficiency is maximized and may exceed unity when the structural and acoustic wavelengths are approximately equal. The frequency at which this occurs is called the critical frequency and can be shifted with structural modifications. This has proven to be an effective way to reduce noise. The standard radiation efficiency measurement is comprised of an intensity scan for sound power measurement and accelerometer array for spatially averaged vibration determination. This method is difficult to apply to lightweight structures, complicated geometries, and when acoustic sources are in close proximity to one another. Recently, robust particle velocity sensors have been developed. Combined with a small microphone in the same instrument, particle velocity and sound pressure can be measured simultaneously and at the same location. This permits radiation efficiency to be measured using a non-contact approach with a single sensor. A suggested practice for measuring radiation efficiency has been developed and validated with several examples including two flat plates of different thickness, an oil pan, and components on a running small engine. KEYWORDS: acoustic radiation efficiency, PU probe, particle velocity, coincidence frequency

Steven Conner Campbell April 22, 2019



By

Steven Conner Campbell

Dr. D. W. Herrin

Director of Thesis

Dr. Alexandre Martin

Director of Graduate Studies

April 22, 2019

Date

iii

ACKNOWLEDGEMENTS

First, I would like to thank God for the capability and knowledge to complete this thesis.

Second, I would like to thank all of the professors I’ve had at UK, especially Dr. David

Herrin for being an excellent advisor, teacher, and friend. Without his support and

guidance this thesis would not be possible. I would like to openly thank Dr. Tim Wu and

Dr. John Baker for their time on my defense committee and all that I have learned from

them during this journey.

To all of my friends in the Acoustics lab at UK, I thoroughly appreciate all of the

experiences, lessons, and fun times we have had over these past few years. I have learned

a tremendous amount of knowledge from each of you. Without this knowledge, I

wouldn’t be where I am today.

I also would like to extend gratitude to all of the members of the Vibro-Acoustic

Consortium, especially to Brett Birschbach and Pat Crowley of Briggs & Stratton

Corporation. The hands-on knowledge and skills learned in the NVH lab has been crucial

to my development as an engineer.

Lastly, I would like to thank my parents Steve and Tammy Campbell, sister Katie

Campbell, and wife Tyla Campbell for all of the support, love, and encouragement

throughout the years. Without them, this work would not be possible.

iv

TABLE OF CONTENTS

ACKNOWLEDGEMENTS .............................................................................................. III

TABLE OF CONTENTS .................................................................................................. IV

LIST OF FIGURES ......................................................................................................... VII

CHAPTER 1 INTRODUCTION ................................................................................. 1

CHAPTER 2 BACKGROUND AND LITERATURE REVIEW ............................... 6

2.1 Radiation Efficiency Equation .................................................................................. 6

2.2 Surface Velocity Determination .............................................................................. 10

2.3 Sound Power Determination ................................................................................... 11

2.4 The Microflown PU Probe ...................................................................................... 13

CHAPTER 3 EXPERIMENTAL METHODS .......................................................... 20

3.1 Introduction to Experimental Methods ................................................................... 20

3.2 PU Probe Calibration .............................................................................................. 21

3.2.1 Sound Pressure Calibration .............................................................................. 21

3.2.2 Particle Velocity Calibration ............................................................................ 23

3.2.3 Sound Intensity Comparison ............................................................................ 24

3.3 Aluminum Plate Case .............................................................................................. 26

3.3.1 Aluminum Plate Sound Power Test.................................................................. 26

3.3.2 Aluminum Plate Surface Velocity Test ............................................................ 28

3.3.3 Aluminum Plate Radiation Efficiency .............................................................. 30

3.4 Stainless-Steel Plate Case........................................................................................ 31

3.4.1 Stainless-Steel Sound Power Test .................................................................... 31

3.4.2 Stainless-Steel Surface Velocity Test ............................................................... 33

v

3.4.3 Stainless-Steel Radiation Efficiency ................................................................ 34

3.5 Oil Pan Case ............................................................................................................ 35

3.5.1 Oil Pan Sound Power Test ................................................................................ 35

3.5.2 Oil Pan Surface Velocity Test .......................................................................... 37

3.5.3 Oil Pan Radiation Efficiency ............................................................................ 38

3.6 Gas Tank Case ......................................................................................................... 39

3.6.1 Gas Tank Sound Power Test ............................................................................ 39

3.6.2 Gas Tank Surface Velocity Test ....................................................................... 42

3.6.3 Gas Tank Radiation Efficiency......................................................................... 43

CHAPTER 4 RESULTS AND DISCUSSION .......................................................... 45

4.1 Discussion on Surface Velocity .............................................................................. 45

4.2 Surface Velocity Corrections .................................................................................. 47

4.2.1 Aluminum Plate Velocity Corrections ............................................................. 47

4.2.2 Stainless-Steel Plate Velocity Corrections ....................................................... 48

4.2.3 Oil Pan Velocity Corrections ............................................................................ 50

4.2.4 Gas Tank Velocity Corrections ........................................................................ 51

4.3 Radiation Efficiency with Surface Velocity Corrections ........................................ 53

4.3.1 Aluminum Plate Corrected Radiation Efficiency ............................................. 53

4.3.2 Stainless-Steel Plate Corrected Radiation Efficiency ....................................... 54

4.3.3 Oil Pan Corrected Radiation Efficiency ........................................................... 54

4.3.4 Gas Tank Corrected Radiation Efficiency ........................................................ 55

CHAPTER 5 CONCLUSIONS AND FUTURE WORK .......................................... 57

5.1 Conclusions ............................................................................................................. 57

5.2 Future Work ............................................................................................................ 58

vi

REFERENCES ................................................................................................................. 59

VITA ................................................................................................................................. 64

vii

LIST OF FIGURES

Figure 2.1 – Radiation efficiency as a function of frequency for plates of varying

dimensions [10]. .................................................................................................................. 8

Figure 2.2 – Radiation efficiency experiments according to ISO-7849. .......................... 10

Figure 2.3 – Signal to noise issue with traditional two-mic intensity probe. If Source B is

much stronger than Source A, intensity measured in the direction of interest is “drown

out”. ................................................................................................................................... 13

Figure 2.4 – Microflown PU probe μ-sensor design. Two hot wires separated by a small

spacing. As current is placed across the bridge, the wires heat up [35]. .......................... 14

Figure 2.5 – Microflown thermal mechanics. As air flows across S1 and S2, a

temperature drop causes a differential electrical resistance variation [40]. ...................... 15

Figure 2.6 – Test setup for PU probe calibration in an anechoic chamber. ...................... 16

Figure 2.7 – Test setup for PU probe calibration in impedance tube. .............................. 17

Figure 3.1 – Measured sound pressure sensitivity of the microphone in the PU probe, 0-

10000 Hz. .......................................................................................................................... 22

Figure 3.2 – Measured phase difference between of the microphone in the PU probe and a

quarter inch microphone, 0-10000 Hz. ............................................................................. 22

Figure 3.3 – Measured particle velocity sensitivity of the velocity sensor in the PU probe,

0-10000 Hz........................................................................................................................ 23

Figure 3.4 – Measured phase difference between of the velocity sensor in the PU probe

and a quarter inch microphone, 0-10000 Hz. .................................................................... 24

Figure 3.5 – Electromagnetic shaker used to excite aluminum plate for intensity

measurements. ................................................................................................................... 24

Figure 3.6 – Intensity scan results for PU probe and two-microphone method from 100-

6000 Hz. ............................................................................................................................ 25

viii

Figure 3.7 – Aluminum plate attached to wooden structure with shaker attached inside.

Plate thickness of 3.175 mm. ............................................................................................ 26

Figure 3.8 – Radiated sound power for the aluminum plate under white noise excitation.

Frequency range of 10 - 6000Hz. ..................................................................................... 27

Figure 3.9 – Aluminum plate sound power map for summed third-octave bands 100 –

5000 Hz. Color scale is 10 dB red to blue. ....................................................................... 28

Figure 3.10 – Surface velocity comparison between PU probe and accelerometer array on

aluminum plate. 10-6000 Hz............................................................................................. 29

Figure 3.11 – Comparison of radiation efficiency for aluminum plate. ........................... 30

Figure 3.12 – Stainless steel plate test setup. Stainless plate thickness 1mm. .................. 31

Figure 3.13 – Sound power measurements for stainless steel plate, 10-6000 Hz. ............ 32

Figure 3.14 – Total sound power measurements for stainless steel plate from 100-5000

Hz, summed 1/3 octave bands. Same 10 dB scale as in Figure 3.9. ................................. 32

Figure 3.15 – Average surface velocity results for stainless steel plate configuration. 10-

6000 Hz. ............................................................................................................................ 33

Figure 3.16 – Radiation efficiency results for both standard and PU probe on the

stainless-steel plate, 10-6000 Hz....................................................................................... 34

Figure 3.17 – Aluminum oil pan mounted to massive mounting block to simulate engine

block boundary conditions. Stinger location is circled in red. .......................................... 35

Figure 3.18 – Imaginary box constructed around the oil pan for sound intensity scan.

Imaginary surfaces are 30 cm from each face of the pan. ................................................ 36

Figure 3.19 – Oil pan sound power results from 100-6000 Hz. ....................................... 37

Figure 3.20 – Comparison of surface velocity results for aluminum oil pan from 100-

6000 Hz. ............................................................................................................................ 38

Figure 3.21 – Oil pan radiation efficiency results from 100-6000 Hz for the PU probe and

standard methods. ............................................................................................................. 39

ix

Figure 3.22 – 420cc engine gas tank. Notice that only 4 sides of the tank are exposed and

have measurable contributions. ......................................................................................... 40

Figure 3.23 – 420cc engine gas tank sound power results in third-octave bands, 125-5000

Hz. ..................................................................................................................................... 42

Figure 3.24 – Gas tank surface velocity results for the 420cc engine. 125-5000 Hz. ...... 43

Figure 3.25 – Third-octave band frequency plot for gas tank radiation efficiency results

from 125- 5000 Hz. ........................................................................................................... 44

Figure 4.1 – Aluminum plate Patch 6, ratio of surface velocity and particle velocity

measured at various distances away. 0-5000 Hz, third-octave bands. .............................. 45

Figure 4.2 – Transfer function between particle velocity at 0.5 cm away and surface

velocity at Patch 6 for aluminum test case. 100-6000 Hz................................................. 47

Figure 4.3 – Corrected velocity measurements for the aluminum plate test case from 100-

6000 Hz. Notice that the FRF-Correction Method for the PU probe yields higher accuracy

than the uncorrected particle velocity. .............................................................................. 48


velocity at Patch 6 for stainless-steel test case. 100-6000 Hz........................................... 49

Figure 4.5 – Corrected velocity measurements for the stainless-steel plate test case from

100-6000 Hz...................................................................................................................... 49


velocity at Patch 8 for oil pan test case. 100-6000 Hz. ..................................................... 50

Figure 4.7 – Corrected velocity measurements for the oil pan test case from 100-6000 Hz.

........................................................................................................................................... 51


velocity at Patch 2 on the top of the gas tank. 125-5000 Hz, third-octave bands. ............ 52

Figure 4.9 – Corrected velocity measurements for the gas tank from 100-6000 Hz. ....... 52

Figure 4.10 – Radiation efficiency for aluminum plate after particle velocity correction,

100-6000 Hz...................................................................................................................... 53

x

Figure 4.11 – Radiation efficiency for stainless-steel plate after particle velocity

correction, 100-6000 Hz. .................................................................................................. 54

Figure 4.12 – Radiation efficiency for stainless-steel plate after particle velocity

correction, 100-6000 Hz. .................................................................................................. 55

Figure 4.13 – Radiation efficiency for the gas tank after particle velocity correction, 125-

5000 Hz. ............................................................................................................................ 56

1

CHAPTER 1 INTRODUCTION

Noise control engineers strive to reduce the sound radiated from machinery in an effort to

manufacture a product that is quieter. This in turn allows a company to vend a product

that is not only quieter but also safer and more marketable. Machinery noise primarily

results from combustion or mechanical mechanisms (piston slap, gear impact, etc.)

producing high forces. These harmonic forces produce structural vibration which in turn

vibrates the air next to the structure. These airborne vibrations propagate away from the

structure and produce what is commonly referred to as noise. It follows that machinery

noise can attenuated by 1) reducing the forces which produce the vibration, 2) reducing

the vibration by making modifications to the structure, 3) by blocking the path from

machinery to receiver using barriers, or 4) reducing how efficiently the structure radiates

noise.

Structural vibration is the direct result of the forces acting on a structure. By reducing

internal forces, vibration can be reduced by a proportional amount. This is accomplished

by two main methods; controlling operating conditions and changing mechanical design.

Operating conditions of mechanical equipment include firing frequency, crank angle,

engine speed, etc. While these operating conditions are normally optimized to improve

performance, they can also be adjusted to reduce noise. Noise reduction in this case is

accomplished by controlling operating conditions to lower the dynamic force amplitudes

on the structure or avoid exciting resonant frequencies of the system. Resonance occurs at

natural frequencies where systems have high vibrational amplitudes even if dynamic

forces are low. These frequencies are primarily determined by the mass and stiffness of

the structure.

At a resonant frequency, vibration amplitude is high. Avoiding input force harmonics that

correspond with these frequencies, reduces the total force experienced by the structure, in

turn reducing noise. For example, if a single-cylinder engine has an operating speed of

3600 RPM this corresponds to a 60 Hz engine order. If the engine design has a resonance

at this 60 Hz frequency, high vibration amplitude will be likely. By adjusting the

operating speed or structure, engine harmonics will no longer correspond to natural

2

frequencies of the structure and a significant noise reduction may be achieved at the

harmonic frequencies of the inputs.

Controlling internal forces and operating conditions is not the only way to reduce

radiated noise. Noise can also be attenuated by making structural modifications that

change system mechanical properties. By changing mass and stiffness, system resonances

can be avoided by shifting natural frequencies higher and lower in frequency. Natural

frequencies are moved higher in frequency if the stiffness is increased or the mass is

decreased. The converse occurs if stiffness is decreased and mass increased. Stiffness is

most commonly increased by adding ribs or increasing thickness. While mass and

stiffness directly affect the frequencies at which resonance occurs, damping reduces the

amplitude of vibration at the system natural frequencies. Damping is increased by adding

constrained layer damping treatments or may be introduced at attachment points between

components.

Alternatively, changes can be made to the acoustic path by adding obstructions between

the source and receiver. This is done by understanding the path that noise propagates as it

travels from the source to the receiver. By shielding an operator from noise via barriers,

partitions or enclosures, the sound propagation path is altered, interrupting the generated

sound. These treatments work best when the receiver point is completely enclosed from

the acoustic source or treatments are placed in areas that offer maximum attenuation.

These treatments offer various benefits and are quite effective, but in many cases are

large and expensive to construct.

A less obvious approach to reduce the radiated noise is to attempt to reduce how

effectively the structure radiates noise. Radiated sound is highly dependent on material

and geometric properties of a structure. When an excited structure is vibrating at a

structural wavelength much lower than the acoustic wavelength, there is cancellation of

sound at the surface.

Radiation efficiency is a measure used to characterize how effectively a structure

radiates noise. Radiation efficiency is low at low frequencies then sharply rises when the

3

structural and acoustic wavelengths are similar in length. This frequency is commonly

referred to as the coincidence frequency (𝑓𝑓𝑐𝑐).

Noise can sometimes be controlled by shifting the coincidence frequency higher in

frequency and away from operating frequencies and their first several harmonics. This is

normally accomplished by increasing the compliance of the structure. However, this must

be done with care because increasing compliance necessarily entails an increase in the

vibration amplitude. In addition, this approach normally cannot be applied on a load

bearing structure without adversely affecting the durability. Adding damping to a

structure changes the amplitude of vibration but does not affect radiation efficiency. On

the other hand, the locations of the input forces may affect radiation efficiency since the

deformation shape is affected.

Radiation efficiency can be determined using a combination of structural finite element

analysis and acoustic boundary or finite element analysis prior to prototyping. After

prototyping, radiation efficiency can be measured. Direct measurement is sometime

advantageous because simulation depends on having correct material properties,

boundary conditions at connections, and input forces. Experimental methods also reduce

the amount of time needed to determine radiation efficiency and find the coincidence

frequency of the system. Simulation for radiation efficiency depends on having adequate

structural and acoustic models that are coupled with one another correctly. Describing the

correct forcing functions of a complex structure can also be incredibly difficult in

simulation without adequate knowledge of the vibratory dynamic excitations. Once the

coincidence frequency is obtained, structural modifications can be performed, and

changes can be observed via performing the experiment again or using a simulation to

correlate the change.

Current methods for determining radiation efficiency experimentally utilize two main

experiments; a vibratory test for surface velocity determination and an acoustic test for

radiated sound power. This two-part method requires a combination of multiple acoustic

and vibration sensors. Normally, a large number of sensors and channels are required to

4

expedite the measurement. However, accelerometers can mass load the structure

corrupting the measurement.

Recently, robust particle velocity probes have been developed that accurately measure

particle velocity. They are small and can be positioned close to a measurement surface.

They have the advantage of being highly directional. The particle velocity sensor has

been combined with a small hearing aid microphone. The combination sound pressure

and particle velocity sensor is referred to as a PU probe. By measuring particle velocity

and sound pressure simultaneously, sound power can be measured and surface vibration

can be approximately measured since the sensor is small and can be positioned next to

the vibrating source. The advantages of the PU probe are several. 1) It is a non-contact

sensor so the modal character of the structure is not changed due to mass loading of the

sensor. 2) Sound intensity measurements with the combination sound pressure and

particle velocity probe are extremely directional and are accurate in a sound field with

nearby sources. 3) Radiation efficiency can be determined for separate components along

with the entire structure. 4) Both quantities needed for a radiation efficiency calculation

can be measured (sound power and vibration) simultaneously.

The objective of this research is to develop protocol for measuring radiation efficiency

with the combination sound pressure and particle velocity sensor or PU probe.

Measurement with the PU probe is compared against traditional measurement

approaches. A possible protocol is developed and tested on several examples. The

objectives of the research are as follows.

Objectives:

1. Test the accuracy of the PU probe for measurement of surface velocity by

comparing it to accelerometer measurements.

2. Test the accuracy of the PU probe for measuring sound intensity by comparing to

the sound intensity scanning approach

3. Test the accuracy for measuring radiation efficiency with the PU probe by

comparing to the standard approach defined in ISO-7849 [1].

4. Develop a protocol for determining radiation efficiency with the PU probe.

5

5. Develop a simple protocol for accurately adjusting a particle velocity

measurement at some distance away from a source to the actual surface velocity.

6. Qualify the method by comparing results on four different structures of varying

shape, thickness, and material.

7. Draw several conclusions and suggest future research.

An outline for the remainder of this work is as follows. Chapter 2 provides a literature

review of past work on both radiation efficiency and the PU probe. Chapter 3 details the

experimental methods utilized to determine radiation efficiency on various geometries

along with an initial comparison between measurement techniques. Chapter 4 offers a

discussion on correcting velocity measurements with the PU probe and a final analysis of

radiation efficiency results. Chapter 5 offers suggestions for future research, outlines the

importance of this work, and concisely summarizes the key takeaways from previous

chapters.

6

CHAPTER 2 BACKGROUND AND LITERATURE REVIEW

2.1 Radiation Efficiency Equation

Radiation efficiency for a structure is defined as the ratio between the radiated sound

power and the equivalent power of a baffled piston with the same surface area and

spatially average vibratory response [2]. Acoustic radiation efficiency is defined as

𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑊𝑊

𝜌𝜌𝜌𝜌𝑆𝑆𝑡𝑡𝑡𝑡𝑡𝑡�̅�𝑣2 (2.1)

where 𝑊𝑊 is the airborne sound power emitted by the structure, �̅�𝑣2is the spatially averaged

RMS value of velocity across the surface, 𝑆𝑆𝑡𝑡𝑡𝑡𝑡𝑡 is the total surface area, 𝜌𝜌 is the mass

density of fluid, and 𝜌𝜌 is the speed of sound [3]. A piston in a baffle is a very efficient

sound radiator and is very much like a loudspeaker. Moreover, the sound power is easily

calculated using the simple expression in the denominator of Equation 2.1. However, a

piston is not the most efficient radiator and thus radiation efficiency may sometimes

exceed 1.

The radiation efficiency of flat panels (plates) [4-7] is well understood. Panels radiate

sound effectively whenever the acoustic wavelength is similar in length to or shorter than

the structural wavelength. The acoustic wavelength is defined as

𝜆𝜆𝑟𝑟 = 𝜌𝜌𝑓𝑓 (2.2)

where 𝜌𝜌 is the speed of sound and 𝑓𝑓 is frequency, With this relationship, acoustic

wavelength is proportional to 1/𝑓𝑓 [8]. The bending stiffness of a thin plate can be

defined as

7

𝐵𝐵 =

𝐸𝐸ℎ3

(12[1 − 𝑣𝑣2]) (2.3)

where 𝐸𝐸 is Young’s modulus, 𝑣𝑣 is Poisson’s ratio, and ℎ is thickness of the panel. The

panel bending wave speed, 𝜌𝜌𝑝𝑝 , is given as

𝜌𝜌𝑝𝑝 = �

𝐵𝐵𝜔𝜔2

𝜌𝜌𝑚𝑚ℎ�

14 (2.4)

where 𝜔𝜔 is angular frequency, ℎ is plate thickness, and 𝜌𝜌𝑚𝑚 is the panel surface density

[9]. This implies that for a bending plate, the structural wavelength (𝜆𝜆𝑝𝑝) is proportional to

1/�𝑓𝑓.

For low frequencies, 𝜆𝜆𝑝𝑝 ≪ 𝜆𝜆𝑟𝑟, the acoustical wavelength will always be larger than the

structural wavelength and the panel bending waves produce positive and negative sources

which cancel one another out. Radiation efficiency is low at these frequencies. At high

frequencies, (𝜆𝜆𝑝𝑝 ≫ 𝜆𝜆𝑟𝑟), there is little cancellation and the radiating plate acts like a set of

uncorrelated point sources.

Radiation efficiency increases sharply when the structural and acoustic wavelengths are

nearly equal in length. This frequency is commonly referred to as the coincidence

frequency (𝑓𝑓𝑐𝑐). At this frequency, acoustic and flexural waves have the same wave speed

and wave length causing sound radiation to increase. Figure 2.1 denotes this phenomenon

for various flat plates on a log scale. Notice that as frequency increases to the coincidence

frequency, radiation efficiency is maximized. By varying the plate panel perimeter, 𝑃𝑃,

surface area 𝑆𝑆, and thickness ℎ, radiation efficiency at frequencies below the coincidence

frequency can be adjusted.

8

Coincidence frequency is a function of the material properties, plate thickness, and the

speed of sound of the gas. Combining Equations 2.2 and 2.4, coincidence frequency can

be expressed as

𝑓𝑓𝑐𝑐 =

𝜌𝜌2

2𝜋𝜋�12(1 − 𝜈𝜈2)𝜌𝜌𝑠𝑠

𝐸𝐸ℎ3 (2.5)

where 𝐸𝐸 is the elastic modulus of the plate, 𝜌𝜌𝑠𝑠is the surface density in units of mass per

unit area, 𝑣𝑣 is the Poisson’s ratio of the plate, and ℎ is plate thickness [11]. From

Equation 2.5, it is evident that coincidence frequency is not dependent on force

amplitude. Rather, coincidence frequency can be altered by modifying the material

properties and especially thickness of the plate. If the stiffness is increased strategically

by adding ribs, the coincidence frequency will increase. Conversely, the coincidence

frequency will be reduced if mass is added carefully. That being said, the most effective

Figure 2.1 – Radiation efficiency as a function of frequency for plates of varying dimensions [10].

9

method for changing the coincidence frequency is to change the thickness of a panel. The

bending stiffness of a panel is proportional to the thickness cubed whereas mass is

proportional to thickness. Damping, on the other hand, only has a small effect on

coincidence frequencies and radiation efficiency. It reduces the vibration amplitude and

the resulting sound power from a time-varying force [12], but radiation efficiency is

unchanged.

Consideration of radiation efficiency has been proven beneficial in designing gearbox

and drivetrain housings [13-14], and engine components like oil pans [15]. Intuitively,

stiffening a structure will result in less sound radiation. However, it is sometimes better to

reduce stiffness so that the coincidence frequency will be above the major source

harmonics. Load bearing structures like engine blocks or supercharger housings must be

stiff for durability reasons. However, non-load bearing structures like oil pans and some

housings may be thin or more compliant. The structure can then be designed to maximize

the coincidence frequency while still making sure that durability requirements are met.

Another interesting application of radiation efficiency is the design of an acoustic guitar.

In contrast to the previous case, musical instruments need to radiate sound in a certain

way or level to meet sound quality expectations. By understanding how geometry,

material properties, and bracing affects the radiation efficiency of a guitar, a

manufacturer can produce a more desirable product. Comparisons between the radiation

efficiency of various acoustic guitars have been made in literature [16].

The procedure for determining radiation efficiency in a simulation model is

straightforward. Structural finite element analysis is first performed to determine the

structural vibration. This analysis is predicated on knowing input forces, damping, and

assigning representative boundary conditions. The structural analysis is followed by

acoustic finite or boundary element analysis to determine the radiated sound power

[14,17,18]. Once sound power and structural vibration are known, radiation efficiency is

readily calculated for the system as a whole or individual panels.

Though the analysis process is straightforward, input forces are often not known until a

prototype has been manufactured and operated. Moreover, connections at bolt locations

10

are difficult to model realistically. Moreover, thin components like shields and valve

covers deform when they are bolted or riveted changing the structural properties. Hence,

it is sometimes simpler to measure radiation efficiency after the component prototype has

been manufactured. The main advantages are that the machinery can be running under

normal operating conditions and no simplifications are made for simulation purposes.

Measurement of radiation efficiency is a two-step process. From Equation 2.1, it can be

seen that acoustic sound power and average surface velocity must be determined. A

standard procedure for conducting the experiment is provided in ISO-7849 [19]. 1) The

vibration on the surface of the machine is measured using accelerometers. 2) The radiated

sound power is measured at a distance away from the source using a sound intensity scan.

The test is illustrated in Figure 2.2.

2.2 Surface Velocity Determination

The most common method of measuring the surface velocity is to attach several

accelerometers to the vibrating structure. The velocity amplitude (𝑣𝑣𝑗𝑗) is determined using

𝑣𝑣𝑗𝑗 = 𝑎𝑎𝑗𝑗

2𝜋𝜋𝑓𝑓 (2.6)

where 𝑎𝑎𝑗𝑗 is the acceleration amplitude and 𝑓𝑓 is the frequency in Hz. The spatially

averaged vibration for a non-uniformly distributed sensor array can be expressed as

Figure 2.2 – Radiation efficiency experiments according to ISO-7849.

11

�̅�𝑣 =

1𝑆𝑆𝑡𝑡𝑡𝑡𝑡𝑡

�𝑆𝑆𝑗𝑗𝑎𝑎𝑗𝑗

2𝜋𝜋𝑓𝑓

𝐾𝐾

𝑗𝑗=1

(2.7)

where 𝐾𝐾 is the number of measurements and 𝑆𝑆𝑗𝑗 is the surface area of each patch. One

disadvantage of using accelerometers is that they can mass load a structure modifying its

modal frequencies. This is especially the case for panels including thin plastic engine

covers, some oil pans, and acoustic guitars.

2.3 Sound Power Determination

Sound power must be measured to obtain the numerator in Equation 2.1. One method that

is commonly used to determine the sound power radiated is the sound intensity scan. The

sound intensity can be averaged over a surface by roving the probe and taking care to

evenly sample the sound intensity over a surface. Sound intensity can also be sampled at

individual points though the former approach is normally used. The sound intensity is

expressed as

𝐼𝐼�̅�𝑛 = 𝑅𝑅𝑅𝑅⟨𝑃𝑃�,𝑈𝑈�𝑛𝑛∗⟩ (2.8)

with 𝑃𝑃� is the sound pressure and 𝑈𝑈�𝑛𝑛∗ is the complex conjugate of particle velocity [20,

21]. Due to difficulty in measuring particle velocity directly, the sound intensity is

normally determined using two closely space microphones. The particle velocity can be

measured accurately parallel to the microphones. The sound intensity is expressed as

𝐼𝐼�̅�𝑛 =

�𝑃𝑃�1𝑃𝑃�2�𝜔𝜔𝜌𝜌𝑡𝑡𝑑𝑑

sin(𝜑𝜑1 − 𝜑𝜑2) (2.9)

12

where 𝑑𝑑 is the separation distance and the difference between 𝜑𝜑1 and 𝜑𝜑2 is the phase

difference between microphones [22, 23]. In order for the measurement to be accurate,

the two microphones must be phase calibrated with respect to one another. Normally, the

sound intensity is scanned over a surface. To determine the total sound power through a

scanned surface, the sound intensity is multiplied by the surface area of the surface

scanned. If 𝑁𝑁 surfaces surround a source, the sound power can be expressed as the sum of

the 𝑁𝑁 sound powers [24]. This is expressed as

𝑊𝑊 = � 𝐼𝐼�̅�𝑛𝑑𝑑𝑆𝑆 ≈ �𝐼𝐼�̅�𝑛∆𝑆𝑆𝑖𝑖

𝑁𝑁

𝑖𝑖=1

𝑆𝑆 (2.10)

where 𝑆𝑆𝑖𝑖 is the surface area for each patch.

The protocol for measurement of sound intensity scanning is provided in ISO-9614-2

[25]. The proper protocol for the method has been discussed in the literature [26-28]. It is

especially noteworthy that maximum frequency for accurate measurement is a function of

the separation distance between the two microphones. In addition, the microphones must

be phase matched or a phase calibration step must be performed prior to measurement.

The method is prone to problems if there is a strong source in a direction transverse to the

line formed by the two microphones as illustrated in Figure 2.3. In that case, the phase

difference between microphones is difficult to measure accurately due to signal to noise

issues.

13

2.4 The Microflown PU Probe

Acoustic particle velocity is one of two quantities needed to determine sound power of an

acoustic disturbance (the other being sound pressure). Particle velocity is defined as the

volume flow divided by the fluid surface in which the acoustic wave propagates [29].

Historically, acoustic particle velocity is difficult to measure and was not directly

measured until recently, unlike sound pressure which is easily obtainable with

microphones.

Particle velocity can now be measured directly with the advent of particle velocity

sensors [30]. The Microflown PU probe, in particular, is commercially available after

extensive development work. The PU probe consists of two main elements – a

Microflown (particle velocity sensor) for measuring particle velocity and a microphone

for sound pressure. The Microflown or μ-sensor is made of two thin closely spaced wires

with a conductive metal covering over them [31]. This sensor directly measures particle

velocity. This is accomplished by use of thermal principles [32, 33].

Figure 2.3 – Signal to noise issue with traditional two-mic intensity probe. If Source B is much stronger than Source A, intensity measured in the direction of interest is “drown

out”.

14

By applying a voltage across the metal conductor, the parallel wires heat up. By

measuring the temperature difference between the wires, particle velocity can be

determined [34]. This is very much like a hot wire anemometer sensor. Figure 2.4 shows

a typical Microflown design [35]. During operation, the two parallel wires are heated up

to above 200°C [36]. As air oscillates across the bridge, one wire is cooled more than the

other [37]. This is dependent on the direction of the particle velocity [38]. By utilizing

temperatures sensors to measure both positive and negative temperature drops across the

wires, particle velocity amplitude can be measured [39]. Since the direction of air motion

produces a temperature change across the wires in a specific direction, the probe is

directional. A schematic of the sensor is shown in Figure 2.5.

With the Microflown and a miniature microphone both integrated into the same

packaging, the PU probe has the capability to measure sound intensity directly [41].

Accurate measurement of sound intensity with this probe relies on proper calibration of

both the particle velocity sensor and microphone in the PU probe.

Figure 2.4 – Microflown PU probe μ-sensor design. Two hot wires separated by a small spacing. As current is placed across the bridge, the wires heat up [35].

15

Particle velocity is most easily calibrated by utilizing the relationship between particle

velocity and sound pressure in the far field. If a loudspeaker is placed on the floor of an

anechoic chamber, a microphone and particle velocity sensor can be located at a specified

distance away from the loudspeaker as shown in Figure 2.6. Assuming the loudspeaker

acts as a monopole, particle velocity can be expressed as

𝑢𝑢(𝑟𝑟) =

𝑝𝑝(𝑟𝑟) 𝜌𝜌𝜌𝜌 × �1 +

1𝑗𝑗𝑗𝑗𝑟𝑟

� (2.11)

where 𝑟𝑟 is the distance from the source, 𝜌𝜌 is the speed of sound, rho is the density, and 𝑗𝑗

is the acoustic wavenumber [42]. Acoustic wavenumber can be expressed as

𝑗𝑗 =𝜔𝜔 𝜌𝜌 (2.12)

Figure 2.5 – Microflown thermal mechanics. As air flows across S1 and S2, a temperature drop causes a differential electrical resistance variation [40].

16

where omega is the angular frequency and c is the speed of sound. Note that the second

term on the right-hand side becomes unimportant as 𝑗𝑗𝑟𝑟 becomes large.

The particle velocity sensor can also be calibrated in an impedance tube so long as plane

wave propagation can be assumed. A schematic of the test setup is shown in Figure 2.7.

By placing the PU probe at a point 𝑥𝑥 in a closed tube with length 𝑙𝑙 and driving the air

with a loudspeaker, particle velocity can be related to sound pressure as [43- 44]

𝑢𝑢(𝑥𝑥) = 𝑝𝑝(𝑥𝑥) ×𝑗𝑗𝜌𝜌𝜌𝜌 tan(𝑗𝑗(𝑙𝑙 − 𝑥𝑥)) (2.13)

This method requires the probe to be carefully positioned in the impedance tube. The

interface between the probe and tube must be well sealed or the measurement will be

compromised.

Monopole

PU Probe

𝑟𝑟

Figure 2.6 – Test setup for PU probe calibration in an anechoic chamber.

17

It is noteworthy that the particle velocity sensor is not able to measure the surface

vibration directly. Particle velocity rapidly decays as the distance from a source is

increased. Very close to a source, the particle velocity and surface vibration are similar

[45]. Ref. [46-48] explore the accuracy of using the particle velocity sensor to measure

surface vibration if the sensor is positioned close to the surface.

For an ideal case of a circular piston in a baffle, the particle velocity can be expressed as

a function of distance (𝑥𝑥) and piston radius (𝑎𝑎) [49]. The particle velocity complex

amplitude can be expressed as

𝑢𝑢𝑛𝑛(𝑥𝑥) = 𝑣𝑣𝑛𝑛�1 − 𝛽𝛽𝑅𝑅−2𝑖𝑖𝑖𝑖� (2.14)

with

𝛽𝛽 =

𝑥𝑥√𝑥𝑥2 + 𝑎𝑎2

(2.15)

and

𝛾𝛾 = 𝑗𝑗 �

√𝑥𝑥2 + 𝑎𝑎2 − 𝑥𝑥2 � (2.16)

Speaker

𝑙𝑙

𝑥𝑥

PU Probe

Anechoic Termination

Figure 2.7 – Test setup for PU probe calibration in impedance tube.

18

where 𝑗𝑗 is the acoustic wavenumber defined as the angular frequency divided by the

speed of sound. If Equation 2.14 is solved for the surface vibration and simplified, the

expression

𝑣𝑣𝑛𝑛(𝑥𝑥) ≈

𝑢𝑢𝑛𝑛(𝑥𝑥)(𝛽𝛽2 − 2𝛽𝛽 cos 2𝛾𝛾 + 1) (2.17)

is obtained. In Equation 2.17, note that the surface and particle vibration are only equal to

each other if 𝛽𝛽 is very small. In order for particle velocity to approximate the surface

velocity, the probe will need to be as close the surface as possible. Note that the

relationship between surface vibration and particle velocity is also a function of

frequency since gamma is a non-dimensional frequency term. Though a relationship

between surface vibration and particle velocity can be obtained for the ideal case of a

baffled piston, an equation relating the two cannot be developed for the general case.

The PU probe can also be used to measure the sound intensity which is normally

measured using a two-microphone approach. The measurement protocol for determining

sound intensity using a two-microphone approach is detailed in ISO-9614-2 [25]. The

accuracy of the PU probe when compared to a two-microphone probe has been explored

in detail and is an accurate alternative intensity probe with similar measurement accuracy

[50-51]. In some cases, the increased directionality of the PU probe leads to more

accurate results than the two-microphone method, especially when various sources are

present and in strongly reactive near fields [52]. The two-microphone method is also very

sensitive to errors with phase mismatching between the two microphones used in the

probe [53]. The PU probe on the other hand, is not as sensitive to these phasing errors

between the velocity sensor and microphone.

The PU probe has been used in many applications ranging from assessing engine noise to

functioning as a battlefield acoustics sensor [54-58]. The application of the PU probe to

radiation efficiency has been explored minimally. Functioning as both a velocity sensor

and intensity probe, the PU probe can determine both fundamental quantities needed to

determine radiation efficiency. Utilizing these capabilities, the PU probe is proposed to

19

simplify measurement of radiation efficiency by measuring both particle velocity and

sound intensity.

20

CHAPTER 3 EXPERIMENTAL METHODS

3.1 Introduction to Experimental Methods

As expanded upon in Chapter 2, determination of radiation efficiency consists of two

separate measurements of radiated sound power and surface vibration. Sound power is

traditionally measured with a sound intensity scan that utilizes a two-microphone probe

and surface vibration is measured with an accelerometer array. The Microflown PU probe

has been proposed as a replacement since both particle velocity and sound pressure can

be measured simultaneously. Since both quantities are measured, the PU probe can be

used to measure sound intensity. The PU probe may also be used to estimate surface

vibration since it can measure particle velocity near a vibrating source.

Four separate test structures were selected for radiation efficiency measurements using

the standard approach and the PU probe. These consisted of the following: 1) a flat

aluminum plate, 2) a flat stainless-steel plate, 3) a ribbed, aluminum oil pan, and 4) a gas

tank connected to a single cylinder engine. These structures were chosen to achieve a

wide variety of geometries, materials, and applications. The flat plates are simple

geometries that are easily understood in literature. On the other hand, the oil pan and gas

tank are much more complex in shape and radiation efficiency is more difficult to

determine with simulation or analytical approaches. This selection includes several types

of sound radiating structures that represent those found commonly in machinery.

By utilizing methods described in ISO-7849, radiation efficiency was measured for each

of the test cases above. This was accomplished by first measuring the sound power

radiated off the surface of the structure with the PU probe. After power was determined,

accelerometers were attached to the structure and average surface velocity was obtained

The PU probe was then moved closer to the vibrating surface, and particle velocity was

measured directly above accelerometer locations. This distance away from the surface

was minimized to reduce the error between the PU probe and the accelerometers.

Radiation efficiency was then calculated for the standard method and the PU probe via

Equation 2.1. For this work, Siemens LMS Test.Lab software and a Siemens SCADAS 8

channel data acquisition (DAQ) system were used to record time data.

21

3.2 PU Probe Calibration

3.2.1 Sound Pressure Calibration

The probe was calibrated in the chamber at the University of Kentucky. Calibration was

undertaken according to the method described in Section 2.4. By placing a loud speaker

in the center of the anechoic chamber and the PU probe at a distance of 1.8 meter away

from the source, sound pressure and particle velocity can be calibrated to microphone

measurements. Since the speaker can be assumed to be a monopole source at this

distance, particle velocity and sound pressure can be related with Equation 2.11 from

Section 2.4 and is shown below.

𝑢𝑢(𝑟𝑟) =

𝑝𝑝(𝑟𝑟) 𝜌𝜌𝜌𝜌 × �1 +

1𝑗𝑗𝑗𝑗𝑟𝑟

� (3.1)

Through placing a quarter inch microphone directly next to the PU probe, sound pressure

can be calibrated simply. First the loudspeaker was excited with white noise from 0-

10000 Hz. Sound pressure was measured at 1.8 meters away from the center of the

speaker with the PU probe and quarter inch microphone simultaneously. The sensitivity

amplitude of the microphone in the PU probe was then determined by dividing the raw

voltage measured by the PU probe’s microphone by the pressure measured by the quarter

inch microphone. Phase was also measured between the two microphones. Sensitivity

results for the microphone in the PU probe are detailed in Figure 3.1 and 3.2.

Measurements were compared to sensitivity curves provided by the manufacturer. There

are noticeable differences at very low frequencies, but this is outside the frequency range

of interest. Differences at low frequencies can be ignored for the purpose of this work. It

was decided to use the calibration curves from the manufacturer though the measured

calibrations could be used as well.

22

Figure 3.1 – Measured sound pressure sensitivity of the microphone in the PU probe, 0-10000 Hz.

Figure 3.2 – Measured phase difference between of the microphone in the PU probe and a quarter inch microphone, 0-10000 Hz.

1.00

10.00

100.00

10.00 100.00 1000.00

Ampl

itude

(mv/

pa)

Frequency (Hz)

Manufacturer Supplied

Experiment

0.0020.0040.0060.0080.00

100.00120.00140.00160.00180.00200.00

10.00 100.00 1000.00

Phas

e (°

)

Frequency (Hz)

Manufacturer SuppliedExperiment

23

3.2.2 Particle Velocity Calibration

Similar to the sound pressure calibration, particle velocity was calibrated for the PU

probe. While the sound pressure is a straightforward comparison to a quarter inch

microphone, particle velocity must be derived from the sound pressure assuming a

monopole source. By assuming that at 1.8 meter away from the presumed monopole

source, near field effects can be ignored and the particle velocity can be expressed as a

function of sound pressure using Equation 3.1. Particle velocity calibration results are

compared to analytical curves from the manufacturer in Figure 3.3 and 3.4.

Also, the sensitivity of the velocity sensor in the PU probe is lower than the expected

values from the manufacturer in low frequency ranges. The loudspeaker with white noise

excitation could not supply enough power at low frequencies. In addition, the hemi-

anechoic chamber itself is only qualified down to 150 Hz. It was elected to use the

manufacturer's calibration for particle velocity as before though the measured value could

also be used. The manufacturer's calibration is selected because the loudspeaker used

does not provide enough power at low frequencies and is not a perfect point source, and

there will be some diffraction effect at the microphone.

Figure 3.3 – Measured particle velocity sensitivity of the velocity sensor in the PU probe,

0-10000 Hz.

0.00

0.01

0.10

1.00

10.00

10.00 100.00 1000.00

Ampl

itude

(/)

Frequency (Hz)


24

3.2.3 Sound Intensity Comparison

The measurement of sound intensity was also checked for the PU probe by comparing to

the two-microphone approach. Two microphones are spaced closely together and sound

pressure is measured at both positions. Sound intensity is calculated from the two

pressure measurements using Equation 2.9.

Figure 3.4 – Measured phase difference between of the velocity sensor in the PU probe and a quarter inch microphone, 0-10000 Hz.

Figure 3.5 – Electromagnetic shaker used to excite aluminum plate for intensity measurements.

-200.00-150.00-100.00-50.00

0.0050.00

100.00150.00200.00

10.00 100.00 1000.00

Phas

e (°

)

Frequency (Hz)


25

An aluminum plate was selected as the test article for the sound intensity comparison. A

schematic of this test setup is shown in Figure 3.5. The plate and support structure are

described in greater detail in Section 3.3.

Once mounted to the support structure, the shaker was used to vibrate the plate with

white noise from 0-6000 Hz. The PU probe was then roved for thirty seconds across the

surface of the plate at 15 cm away. Sound intensity was calculated using Equation 2.8

and time averaged over the surface. Likewise, the two-microphone probe was roved

across the surface of the plate at 15 cm. Sound pressure was measured for each

microphone and sound intensity calculated via Equation 2.19 was time averaged. Results

are shown for each method in Figure 3.6.

The sound intensity measured with the PU probe and two-microphone method are

correlate. Differences between curves at most frequencies are well under 2.5 dB above

250 Hz. These results demonstrate that the PU probe is properly calibrated. By measuring

sound intensity on this simple baseline case, it can be seen that the PU probe corresponds

well with standard practice. In the remainder of the chapter, the PU probe will be used to

determine the radiation efficiency.

Figure 3.6 – Intensity scan results for PU probe and two-microphone method from 100-6000 Hz.

20

30

40

50

60

70

80

100 1000

Soun

d In

tens

ity (d

B)

Frequency (Hz)

Two-Microphone Method

PU Probe

26

3.3 Aluminum Plate Case

3.3.1 Aluminum Plate Sound Power Test

A flat aluminum plate of thickness 3.175 cm was selected for the initial test case. By

plugging appropriate material properties and thickness into Equation 2.5, the theoretical

coincidence frequency of this plate is around 1300 Hz. The frequency range of interest is

from 0 to 6000 Hz. A 50-lbs electromagnetic shaker was used to drive the panel and is

more than sufficient since the panel is light. Figure 3.7 shows a photograph of the panel

and overall dimensions.

The electromagnetic shaker was positioned inside the box shown in Figure 3.5. The box

was made of 3/4-inch particle board. The plate was affixed to the top of the box using

metallic tape. The shaker was attached to the panel at the position shown in Figure 3.7. It

was located away from the center of the plate to avoid exciting the panel at node

locations though the excitation position should not be as important at higher frequencies.

The radiated sound power from the plate was then measured with the PU probe at

discrete locations. Discrete locations were chosen so that contour plots of the sound

intensity could be prepared using the same data later. The sound intensity scan was

Figure 3.7 – Aluminum plate attached to wooden structure with shaker attached inside. Plate thickness of 3.175 mm.

27

performed at a distance of 15 cm directly above the surface of the plate. Intensity was

measured at the center of each patch point in the 4 x 4 grid shown in Figure 3.7 which

yielded a total of 16 individual sound intensity values.

The time data was taken for thirty seconds at each location with five averages per second

and the frequency resolution was set at 5 Hz. The white noise force excitation was

controlled via Test.Lab and an amplifier.

After obtaining the sound intensity values as the discrete locations, sound power was

calculated off the surface of the vibrating plate using Equation 2.10. Sound intensity was

averaged over the surface of the plate and the multiplied over the area for the scan. Sound

power was calculated and the measured sound power for the aluminum plate is shown in

Figure 3.8.

Sound power was determined at discrete locations above the surface of the plate. Siemens

Test.Lab is capable of displaying the sound power as a contour plot as shown in Figure

3.9. This capability is very helpful for identifying the largest contributing sources. For

Figure 3.8 – Radiated sound power for the aluminum plate under white noise excitation. Frequency range of 10 - 6000Hz.

20

30

40

50

60

70

10 100 1000

Soun

d Po

wer

(dB)

Frequency (Hz)

28

this example, it can be seen that the highest contributions are close to the excitation

location.

3.3.2 Aluminum Plate Surface Velocity Test

To determine radiation efficiency, surface vibration was also measured on the aluminum

plate. This was accomplished using the same test setup. Surface velocity was measured

right after the sound power measurement to ensure that the operating conditions in no

way changed between tests. This uniformity is extremely important – by slightly

adjusting the input level on the amplifier or reapplying the metallic on the plate, surface

velocity and sound power may be different changed between measurements. These errors

should be minimal in this work because care was taken to ensure that neither the input

forcing function or boundary conditions changed between tests.

Moreover, surface velocity was measured with two separate methods; an accelerometer

array and by roving the PU probe near the surface of the plate. For the standard method,

an accelerometer array was directly attached to the surface of the structure at the center of

each patch as shown in Figure 3.7. Acceleration was measured via the accelerometer

Figure 3.9 – Aluminum plate sound power map for summed third-octave bands 100 – 5000 Hz. Color scale is 10 dB red to blue.

29

array for thirty seconds at each center location. The average velocity was then obtained

for the 16 measurements. Dummy masses were utilized to prevent mass loading effects

since only 6 accelerometers were available for the measurement.

For the PU probe measurements of surface velocity, the PU probe was placed 0.5 cm

away from the center of each patch. Since particle velocity rapidly decays as a function of

distance away from a source, distance was minimized to reduce error between the particle

velocity sensor in the PU probe and corresponding accelerometer measurements. To

reduce human error, the PU probe was positioned using a microphone stand at the

specified distance above the vibrating plate. The PU probe was moved to each discrete

location and data was obtained and averaged for 30 seconds. Average particle velocity at

0.5 cm above the plate was then calculated by spatially averaging the data at all 16

locations.

Comparisons between the average surface velocity measured with the accelerometer

array and the PU probe are shown in Figure 3.10. This difference remains fairly constant

with frequency and is approximately 3 dB. This can likely be attributed to the distance

between particle and surface velocity. Note that the results converge at very high

frequencies.

30

40

50

60

70

80

90

10 100 1000

Surfa

ce V

eloc

ity (d

B)

Frequency (Hz)

StandardAccelerometer Array

Figure 3.10 – Surface velocity comparison between PU probe and accelerometer array on aluminum plate. 10-6000 Hz

30

3.3.3 Aluminum Plate Radiation Efficiency

After completing both the surface velocity determination and sound power mapping for

the aluminum plate, radiation efficiency was calculated utilizing Equation 2.1 for both the

standard method and PU probe measurements. Figure 3.11 shows these results. Since the

PU probe measured a lower surface velocity, the calculated radiation efficiency is a few

dB higher than the standard measurement. Hence, the denominator in Equation 2.1 is

lower if the PU probe is used which correspondingly increases the radiation efficiency by

a similar amount.

Note that the radiation efficiency increases to close to unity at around 3000 Hz which is

much higher than the coincidence frequency which is predicted to be 1300 Hz using

Equation 2.5. However, Equation 2.5 does not take into account the boundary conditions

of the plate. In summary, the radiation efficiency error hovers around 3 dB except at the

very high frequencies. As an engineering method, it is an acceptable alternative to ISO-

7849 for this case.

0.001

0.01

0.1

1

10

10 100 1000

Rad

iatio

n Ef

ficie

ncy

Frequency (Hz)

StandardPU Probe

Figure 3.11 – Comparison of radiation efficiency for aluminum plate.

31

3.4 Stainless-Steel Plate Case

3.4.1 Stainless-Steel Sound Power Test

The second test case is much thinner 1 mm thick stainless-steel plate mounted to the

same wooden support structure as before. For this test case, a 3 X 3 set of 9 points was

used for sound power mapping. The test setup is shown in Figure 3.12 and is identical to

the Section 3.3 measurement but with the thinner stainless-steel plate. Per Equation 2.5,

the coincidence frequency is approximately 3700 Hz. From the coincidence frequency

calculation, the stainless-steel plate is anticipated to have a lower radiation efficiency

than the aluminum plate.

Sound intensity was measured with the PU probe in the same manner described in

Section 3.2.1. The plate was excited by the electromagnetic shaker using white noise

from 0 to 6000 Hz. The probe positioned at the center of each patch and sound intensity

was measured. Data was time averaged for 30 seconds at each location. The spatially

averaged sound intensity was then determined over the surface of the plate. The radiated

sound power was then calculated by multiplying the average sound intensity by the area

Figure 3.12 – Stainless steel plate test setup. Stainless plate thickness 1mm.

32

of the scanning surface in a manner analogous to ISO-9614-2. The sound power is plotted

versus frequency in Figure 3.13.

-100

1020304050607080

10 100 1000

Soun

d Po

wer

(dB)

Frequency (Hz)

PU Probe

Figure 3.13 – Sound power measurements for stainless steel plate, 10-6000 Hz.

Figure 3.14 – Total sound power measurements for stainless steel plate from 100-5000 Hz, summed 1/3 octave bands. Same 10 dB scale as in Figure 3.9.

33

Figure 3.14 shows the sound power mapping for the stainless-steel plate. One-third

octave band results are summed in this plot. Note that location around the stinger

contributes most to the overall sound power. However, the contribution likely varies as a

function of frequency so no sweeping conclusions should be made.

3.4.2 Stainless-Steel Surface Velocity Test

After completing the sound intensity mapping for the thinner stainless-steel plate, the

surface vibration methods applied to the aluminum plate were repeated on the new plate.

Accelerometer measurements were made at the center of each patch and the PU probe

was used to measure particle velocity at a distance of 0.5 cm away. A single

accelerometer was roved from position to position. This procedure was likewise followed

for the PU probe. Accelerometer and PU probe measurements were spatially averaged.

Figure 3.15 compares the spatially averaged surface velocity measured with an

accelerometer to the spatially averaged particle velocity measured with the PU probe.

Agreement is similar to the aluminum plate case, and it can be seen that the PU probe

measures a few dB low at most frequencies. By switching from 16 discrete measurement

Figure 3.15 – Average surface velocity results for stainless steel plate configuration. 10-6000 Hz.

102030405060708090

100

100 1000

Surfa

ce V

eloc

ity (d

B)

Frequency (Hz)

Roving Accelerometer

PU Probe

34

locations to 9, accuracy does not seem affected. Also, the effect of mass loading seemed

to be negligible since the accelerometers were removed for PU probe measurements.

3.4.3 Stainless-Steel Radiation Efficiency

The radiation efficiency was determined using both the standard and PU-probe

approaches. Results are compared in Figure 3.16. It can be observed in Figure 3.16 that

radiation efficiency is much lower for the stainless-steel plate as is anticipated. Similar to

the aluminum plate, the lower measured surface velocity using the PU probe results in a

2-4 dB higher radiation efficiency calculation. Notice that the radiation efficiency does

not approach unity up to 5000 Hz..

Figure 3.16 – Radiation efficiency results for both standard and PU probe on the stainless-steel plate, 10-6000 Hz.

35

3.5 Oil Pan Case

3.5.1 Oil Pan Sound Power Test

As seen in the previous sections, the PU probe can function as an alternative method for

radiation efficiency determination. In Sections 3.3 and 3.4, simple geometries in the form

of thin metallic plates were explored. While these plates are typical of plates on

enclosures and HVAC ductwork, most mechanical structures are not so simple. To meet

performance and mechanical expectations, mechanical components frequently have very

complicated geometries. With this in mind, a few industrial applications have been

selected to further evaluate the accuracy of the PU-probe for measurement of radiation

efficiency.

The first of these applications is a ribbed, aluminum oil pan. By functioning as a reservoir

for engine oil, this cover is bolted to an engine block in application. As the engine

operates, internal combustion and mechanical forces propagate through the engine block

to the oil pan which in turn radiates noise. By understanding the radiation efficiency of

the oil pan, the manufacturer can reduce the propagation path between force excitation

and airborne sound power.

Figure 3.17 – Aluminum oil pan mounted to massive mounting block to simulate engine block boundary conditions. Stinger location is circled in red.

36

The ribbed oil pan was mounted to a 32 kg (70 lbs) steel plate. The electromagnetic

shaker utilized in previous sections was selected as the force excitation. The oil pan was

divided into a 3 X 3 grid and measurements were made at the center of each of the 9

patches. The shaker was attached between patches 3 and 6 as shown in Figure 3.17.

Figure 3.17 shows the oil pan attached to the 32 kg steel plate. Note that the oil plan is

bolted to the plate at each of the prescribed mounting holes.

In order to determine the oil pan’s radiation efficiency, a sound intensity scan was first

performed to find radiated sound power. To perform the scan, a cuboid grid was

constructed with surfaces that were 30 cm away from each face of the cover as shown in

Figure 3.18. White noise excitation was used and the PU probe was roved across the

surface of each imaginary plane to determine the sound power. The average sound

intensity was measured through each plane and the sound power was determined by

multiplying the intensity by the area. Data was time averaged for 30 seconds during each

sweep. The sound power is plotted versus frequency in Figure 3.19.

Figure 3.18 – Imaginary box constructed around the oil pan for sound intensity scan. Imaginary surfaces are 30 cm from each face of the pan.

37

3.5.2 Oil Pan Surface Velocity Test

The surface vibration was the measured by roving a single accelerometer along the plate.

Measurements were made at the center of each patch. The oil pan is stiff and massive so

the effect of mass loading was expected to be negligible. Data was collected and

averaged for 30 seconds at teach position. The nine measurement points should be

sufficient according to ISO-7849. The surface area of the oil pan is under 1 m2 and for

this surface area, five measurement points are recommended per ISO-7849 [2].

Particle velocity was measured with the PU probe at a distance of 0.5 cm from the

surface. The PU probe was mounted on a microphone stand to ensure that the distance

between prove and surface was kept constant at 0.5 cm. White noise excitation up to

6000 Hz was input. Data was collected and averaged for 30 seconds at the center of each

patch. The particle velocity was then spatially averaged.

The surface and particle velocity at a distance of 0.5 cm are compared in Figure 3.20. The

PU probe measurements are about 3 dB lower than the surface vibration. This is likely a

result of particle velocity decaying as the distance from the plate increases. Also, it is

notable that the resonant peaks dropped in frequency by about 5 Hz. This is almost

0

20

40

60

80

100 1000

Soun

d Po

wer

(dB)

Frequency (Hz)

Figure 3.19 – Oil pan sound power results from 100-6000 Hz.

38

certainly a result of mass loading. However, this slight reduction in frequency will only

slightly impact the radiation efficiency predictions.

3.5.3 Oil Pan Radiation Efficiency

Using the sound power and surface vibration data, radiation efficiency was calculated

according to Equation 2.1. Radiation efficiency results are plotted in Figure 3.21 for the

frequency range of interest. Results between the standard approach and the PU probe

correlate well though there is approximately a 3 dB difference consistent with the prior

two plate examples. The lower PU probe results are again a result of the lower average

surface vibration measurement using the PU probe.

There are some advantages in using the PU probe in this example. As noted earlier, mass

loading does slightly shift some of the frequency peaks lower in frequency. Additionally,

there is some difficulty in mounting accelerometers to the cover because of the ribbing,

so a non-contact approach is easier to use. Finally, the test case suggests that the radiation

102030405060708090

100

100 1000

Surfa

ce V

eloc

ity (d

B)

Frequency (Hz)

Roving AccelerometerPU Probe

Figure 3.20 – Comparison of surface velocity results for aluminum oil pan from 100-6000 Hz.

39

efficiency measurement can be improved if the particle velocity measurement is adjusted.

This topic will be explored further in Chapter 4.

3.6 Gas Tank Case

3.6.1 Gas Tank Sound Power Test

The final test case considered is a field test where the radiation efficiency of the gas tank

on an internal combustion engine is measured. This was accomplished by considering the

gas tank on an internal combustion engine. The previous plate test cases consisted of one

forcing function (the shaker) and one acoustic source (the plate). The internal combustion

engine (420 cc) has several noise generating components. Some of these components are

in close proximity with each other. The gas tank is a good candidate component because

it receives vibratory energy through other components but is not exposed to larger

dynamic forces like piston slap and combustion.

Measuring the radiation efficiency is difficult for a component because it is difficult to

accurately measure sound power using a sound intensity probe in the presence of other

sources. Nearby sources add noise to the measurement. However, the PU probe is very

0.001

0.01

0.1

1

10

100 1000

Rad

iatio

n Ef

ficie

cny

Frequency (Hz)

StandardPU Probe

Figure 3.21 – Oil pan radiation efficiency results from 100-6000 Hz for the PU probe and standard methods.

40

directional and sound power can be accurately determined even if other sources are

dominant.

Figure 3.22 shows a photograph of the gas tank and the measurement grid. Notice that

the geometry of the gas tank is cuboidal. Four sides of the gas tank are exposed. The

bottom is nestled against the engine block and the left side next to the muffler and intake.

The four exposed surfaces were discretized into a 3 X 3 grid and measurement locations

were positioned at the center of each grid square. An imaginary box, 15 cm (6 in) away

from each exposed surface, was constructed for measuring sound intensity. If the box is

larger, other sources such as the fan and intake manifold will be included in the sound

power measurement. While near field effects are not guaranteed to be avoided, the

selected distance of 15 cm is selected a compromise. This is a common issue faced when

measuring sound intensity in a field with several closely spaced sources.

Typical operating speeds for this engine are in the range of 2000 to 4000 RPM, a safe

steady-state operating speed of 2700 RPM was selected as the operating condition. The

Figure 3.22 – 420cc engine gas tank. Notice that only 4 sides of the tank are exposed and have measurable contributions.

41

engine was mounted to a stand which was in turn rigidly fixed to a bed plate for safety

reasons. The engine speed was monitored with an optical tachometer and was recorded

using a tach channel on the SCADAS. An inertia disk was attached to the crankshaft in

order to load the engine by a small amount. By adding this loading, the inertia disk

simulates being attached to a driveshaft and stabilizes the engine with boundary

conditions similar to actual operation.

Sound intensity was obtained on the running engine using two separate methods. It was

first measured at 15 cm away from each exposed surface of the tank. Sound pressure and

particle velocity were measured normal to each imaginary surface at 15 cm away for

thirty seconds with the PU probe in a sweeping manner. The frequency range of interest

was 125 to 5000 Hz and data was taken in third-octave bands. Third-octave bands are

desirable over narrowband in cases where time harmonic frequencies are dominant. For

the combustion engine, strong harmonics occur at frequencies corresponding to engine

speed. By summing the data in one-third octave bands, the calculated sound power and

radiation efficiency is easier to understand visually on a graph. Sound intensity was

calculated for each surface with Equation 2.8. After intensity was averaged across the

surface of the imaginary box, sound power was obtained via Equation 2.10 by

multiplying average sound intensity by surface area.

Sound intensity was also measured closer to the vibrating surfaces of the gas tank. Even

though near-field effects affect the measurement close to the source, a scaled-down

scanning box at 1.5 cm from each surface of the tank was constructed. By encompassing

a smaller area during the intensity scan, other components generating unwanted

contributions can be eliminated. After the new scanning surface was created closer to the

gas tank, the PU probe was roved for thirty seconds across each surface. Sound pressure

and particle velocity were determined for each surface and sound power was measured as

before.

Results for both the near-field and far-field power are plotted in Figure 3.23. Comparing

the sound power between both scans, large discrepancies are present. The sound power

measured in the far-field is much larger than that measured in the near field especially at

42

frequencies below 630 Hz. By increasing the area of the scanning surfaces, the sound

power measured at a distance of 15 cm is likely contaminated by sources other than the

gas tank. With this in mind, sound power obtained close to the surface of the tank is used

for determining radiation efficiency.

3.6.2 Gas Tank Surface Velocity Test

The surface acceleration was measured using 9 accelerometers. All sensors were attached

to the surface of the tank during all measurements to insure consistency of mass loading.

After one side was completed, the entire array of accelerometers was moved to a different

face on the gas tank. Average acceleration was determined for each face and surface

velocity was obtained using Equation 2.7.

The PU probe was then used to measure particle velocity at the center of each patch 1.5

cm away from the surface of the gas tank. Instead, the PU probe was attached to an

aluminum rod and held in hand. This complex geometry required more finesse in keeping

the probe normal to the tank's surface and use of a microphone stand was unfeasible. As

such, controlling the distance away from the surface of the vibrating tank was difficult

when compared to the plate and oil pans tests.

60

65

70

75

80

85

100 1000

Soun

d Po

wer

(dB)

Frequency (Hz)

Near-Field Far-Field

Figure 3.23 – 420cc engine gas tank sound power results in third-octave bands, 125-5000 Hz.

43

After the particle velocity at 1.5 cm away was obtained at all thirty-six measurement

points, average particle velocity was calculated for the entire exposed surface. Figure

3.24 shows the third-octave band frequency plots for surface velocities obtained with the

accelerometer array and the PU probe.

3.6.3 Gas Tank Radiation Efficiency

Using the surface velocity and sound power measurements at 1.5 cm away from each

surface of the tank, radiation efficiency was calculated according to Equation 2.1. Figure

3.25 compares the radiation efficiency measured using each approach. The error between

the methods is on the order of 10 dB at some frequencies. As anticipated, the radiation

efficiency measured using the PU probe is high due to the inaccurate measurement of

surface vibration. Errors are higher in this case because the PU probe is located further

away from the vibrating surface. However, it was hypothesized that the PU probe results

could be corrected so that correlation was improved.

Figure 3.24 – Gas tank surface velocity results for the 420cc engine. 125-5000 Hz.

60

70

80

90

100

110

100 1000

Surfa

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eloc

ity (d

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Frequency (Hz)

Accelerometer Array

PU Probe

44

0.001

0.01

0.1

1

10

100 1000

Rad

iatio

n Ef

ficie

cny

Frequency (Hz)

StandardPU

Figure 3.25 – Third-octave band frequency plot for gas tank radiation efficiency results from 125- 5000 Hz.

45

CHAPTER 4 RESULTS AND DISCUSSION

4.1 Discussion on Surface Velocity

The results in the prior chapter indicated that particle velocity decays rapidly with

distance from the vibrating surface. This effect was investigated using Patch 6 on the

aluminum plate. The particle velocity was measured at different distances from the

source and compared to surface velocity. The ratio of the measured particle to surface

velocity is shown in Figure 4.1. It can be seen that the ratio decreases significantly with

distance away from the source.

Based on these results, a correction method is proposed to adjust the particle velocity

measured with the PU prove to better match the actual surface velocity. Though an

analytical relationship could be developed, the relationship between particle and surface

velocity likely depends on the surface velocity. Instead, a simple measurement correction

is recommended. The surface velocity 𝑣𝑣𝑛𝑛(𝑥𝑥 = 0) at a position on the vibrating surface is

measured with an accelerometer and compared withthe particle velocity 𝑢𝑢𝑛𝑛(𝑥𝑥) at some

distance away from the surface. A transfer function is measured between the two and the

0.01

0.1

1

100 1000

Parti

cle

to S

urfa

ce V

eloc

ity R

atio

Frequency (Hz)

0.5 cm 8 cm22 cm 45 cm

Figure 4.1 – Aluminum plate Patch 6, ratio of surface velocity and particle velocity measured at various distances away. 0-5000 Hz, third-octave bands.

46

amplitude is taken. With n equal to the patch number, the transfer function 𝐻𝐻 is expressed

as

𝐻𝐻 =

𝑣𝑣𝑛𝑛(𝑥𝑥 = 0)𝑢𝑢𝑛𝑛(𝑥𝑥) (4.1)

This transfer function serves as a distance and frequency-based correction and can be

measured for various distances away from the source. By measuring the average surface

velocity across the entire surface of the source at a constant distance 𝑥𝑥, the average

surface velocity can be determined by multiplying the average particle velocity across the

surface by the transfer function shown in Equation 4.1. This transfer function amplitude

serves as a simple correction for the measured particle velocity. This measurement is

easily completed and can be considered a calibration for the PU probe.

The main concern that can arise from utilizing one point on a vibrating surface to correct

the PU probe is where to place the accelerometer. Regardless of the selected position, it is

inevitable that the position will lie on the node line of certain modes. This lack of

measured vibration will lead to inaccurate data at certain frequencies. There are two ways

to mitigate this issue. One method is to measure the surface vibration at several positions

and average, but that increases the measurement time and complexity. Alternatively, a

running average of the transfer function can be performed to smooth the result. This

method is more advantageous since transfer functions for radiation problems are

anticipated to be smooth. By using a running average, peaks and troughs resulting from

plate resonances will be smoothed.

47

4.2 Surface Velocity Corrections

4.2.1 Aluminum Plate Velocity Corrections

The particle to surface velocity ratio is shown in Figure 4.2 for the aluminum plate.

Particle velocity is measured 0.5 cm from the plate surface. If a 200 Hz running average

is applied, the smoothed curve also shown in Figure 4.2 is obtained. Note that the peaks

and troughs in the narrowband transfer function are smoothed out which yields a smooth

correction curve. It is recommended that the location selected for correction not be too

close to the excitation location or a fixed edge.

With this velocity correction curve, the average particle velocity was corrected. This

correction can be expressed as

𝑣𝑣𝑟𝑟𝑎𝑎𝑎𝑎 = 𝑢𝑢𝑟𝑟𝑎𝑎𝑎𝑎 × 𝐻𝐻 (4.2)

0.1

1

10

100 1000

Ampl

itude

(/)

Frequency (Hz)

Baseline

200 Hz Running Average

Figure 4.2 – Transfer function between particle velocity at 0.5 cm away and surface velocity at Patch 6 for aluminum test case. 100-6000 Hz.

48

where 𝑢𝑢𝑟𝑟𝑎𝑎𝑎𝑎 is the average measured particle at x = 0.5 cm and H is the correction transfer

function. After applying the correction, the surface velocity measured with the PU probe

correlates very well with the surface vibration measured using accelerometers as shown

in Figure 4.3. Differences are less than 2 dB at most all frequencies.

Note that the proposed approach is straightforward and requires minimal additional data.

If the distance from the plate is chosen optimally, it is possible that one measurement

surface will be sufficient. Based on this initial success, the method was used to determine

the surface vibration for the other 3 examples.

4.2.2 Stainless-Steel Plate Velocity Corrections

A similar velocity correction was also applied to the 1 mm stainless-steel plate. The ratio

of the surface to particle velocity is plotted versus frequency in Figure 4.4. A 200 Hz

running average was again applied to smooth out any discontinuities. The correction

curve and even the smoothed curve are not as flat as the result for the 5 mm aluminum

plate. These discontinuities likely arise as a result of the accelerometer being located at

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100 1000

Surfa

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eloc

ity (d

B)

Frequency (Hz)

Accelerometer ArrayCorrected Particle Velocity

Figure 4.3 – Corrected velocity measurements for the aluminum plate test case from 100-6000 Hz. Notice that the FRF-Correction Method for the PU probe yields higher

accuracy than the uncorrected particle velocity.

49

node lines of the mode shapes of the plate. The chance of this occurring increases at

higher frequencies as the structural wavelength decreases.

0.1

1

10

100

100 1000

Ampl

itude

(/)

Frequency (Hz)

Baseline 200 Hz Running Average

Figure 4.4 – Transfer function between particle velocity at 0.5 cm away and surface velocity at Patch 6 for stainless-steel test case. 100-6000 Hz.

102030405060708090

100

100 1000

Surfa

ce V

eloc

ity (d

B)

Frequency (Hz)

Roving Accelerometer

Corrected Particle Velocity

Figure 4.5 – Corrected velocity measurements for the stainless-steel plate test case from 100-6000 Hz.

50

The corrected particle velocity results are compared to the accelerometer measurements

in Figure 4.5. The agreement is acceptable even at higher frequencies. The discrepancies

at 1700 and 2700 Hz result from measuring at node lines on the plate since the surface

vibration is very low at these positions. This results in an over correction, but taking a

running average reduces the amount over correction. One advantage of a particle velocity

measurement is that there are no gaps in vibration data at the node lines.

4.2.3 Oil Pan Velocity Corrections

The particle velocity was likewise corrected for the oil pan test case. Patch 8 was selected

since it was not near the excitation position or the edges. The ratio of the surface

vibration to particle velocity is compared in Figure 4.6 as a function of frequency. A 200

Hz running average is again used and a relatively flat calibration curve is identified.

There are some peaks at higher frequencies. These occur at frequencies where the surface

vibration is low.

Figure 4.6 – Transfer function between particle velocity at 0.5 cm away and surface velocity at Patch 8 for oil pan test case. 100-6000 Hz.

0.01

0.1

1

10

100

100 1000

Ampl

itude

(/)

Frequency (Hz)

Baseline 200 Hz Running Average

51

The error between the corrected and measured particle velocity is shown in Figure 4.7.

Agreement is excellent at most frequencies.

4.2.4 Gas Tank Velocity Corrections

The final test case examined is the gas tank attached to the internal combustion engine.

This example presents a number of challenges that are anticipated in operating

machinery. First, the gas tank is close to several other source components. Secondly, the

gas tank has a complicated geometry. For practical purposes, PU probe measurements

cannot be made at the same distance away from the surface. Measurements were hence

made by hand at approximately 1.5 cm from the surface. Finally, the gas tank is only

driven at the engine harmonic frequencies and not by broadband shaker excitation. For

these reasons, the gas tank test case should test the robustness of the correction approach.

The top surface of the gas tank was used for measuring the correction transfer function. It

is the most exposed surface and it is also flatter than the other surfaces. Patch 2 on the top

of the gas tanks was selected. The transfer function between the surface velocity

measured with an accelerometer and particle velocity measured at 1.5 cm away with the

PU probe was measured in one-third octave bands. No running average was performed in

Figure 4.7 – Corrected velocity measurements for the oil pan test case from 100-6000 Hz.

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100 1000

Surfa

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Frequency (Hz)

Roving AccelerometerCorrected Particle Velocity

52

this case. Figure 4.8 shows the correction which is relatively constant over the full

frequency range from 125 to 5000 Hz.

60

70

80

90

100

110

100 1000

Surfa

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eloc

ity (d

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Frequency (Hz)

Accelerometer Array


Figure 4.9 – Corrected velocity measurements for the gas tank from 100-6000 Hz.

0.1

1

10

100 1000

Ampl

itude

(/)

Frequency (Hz)

Figure 4.8 – Transfer function between particle velocity at 1.5 cm away and surface velocity at Patch 2 on the top of the gas tank. 125-5000 Hz, third-octave bands.

53

The corrected average particle velocity is compared to direct measurement of average

acceleration in Figure 4.9. Agreement is acceptable over the full frequency range of

interest.

4.3 Radiation Efficiency with Surface Velocity Corrections

4.3.1 Aluminum Plate Corrected Radiation Efficiency

The radiation efficiency for the aluminum plate was recalculated using the corrected

particle velocity. The sound power was measured using the PU probe in both cases.

Radiation efficiency is compared in Figure 4.10 It can be observed that agreement is

excellent over the entire frequency range.

0.001

0.01

0.1

1

10

100 1000

Rad

iatio

n Ef

ficie

ncy

Frequency (Hz)

Accelerometer Array


Figure 4.10 – Radiation efficiency for aluminum plate after particle velocity correction, 100-6000 Hz.

54

4.3.2 Stainless-Steel Plate Corrected Radiation Efficiency

The radiation efficiency was also calculated for the 1 mm stainless-steel plate using the

corrected particle velocity. For both cases, the sound power was determined by scanning

with the PU probe. The radiation efficiency is compared in Figure 4.11. These results are

less accurate than those for the aluminum plate, but the correlation is nonetheless

acceptable and will be suitable for engineering purposes.

4.3.3 Oil Pan Corrected Radiation Efficiency

The procedure was then repeated for the oil pan. The radiation efficiencies determined

using the corrected particle velocity and direct accelerometer measurements are

compared in Figure 4.12. Notice that the agreement is excellent except at the higher

frequencies. In this case, the results are likely better using the corrected particle velocity.

This is due to the fact that surface vibration results are too low when the accelerometer is

located at a node line. In addition, there is also a mass loading effect since the natural

frequencies of the oil pan shift slightly when the accelerometer is roved on the plate.

These results suggest that the PU probe may prove advantageous since it is a non-contact

approach.

0.00001

0.0001

0.001

0.01

0.1

1

100 1000

Rad

iatio

n Ef

ficie

ncy

Frequency (Hz)


Figure 4.11 – Radiation efficiency for stainless-steel plate after particle velocity correction, 100-6000 Hz.

55

4.3.4 Gas Tank Corrected Radiation Efficiency

The last case considered is the gas tank attached to the internal combustion engine. The

difficulties of this case were noted earlier in Section 4.2.4. Corrected particle velocity

was again used to determine the radiation efficiency. Radiation efficiency is compared

between corrected PU probe and direct acceleration measurement in Figure 4.13.

Agreement is generally good between the two curves. As an engineering method, the PU

probe measurements are certainly acceptable.

In summary, an alternate method for determination of radiation efficiency has been

proven. By correcting particle velocity measurements with a single transfer function

measurement, surface velocity can be accurately obtained with the PU probe. After

completing a sound intensity scan with the PU probe, sound power can also be

determined. Combining these two measurements and Equation 2.1, radiation efficiency

can be measured accurately. This has been proven on a diverse pool of complex vibrating

structures under various forcing functions. Accuracy for this method is on the order of the

methods proposed in ISO-7849.

0.001

0.01

0.1

1

10

100 1000

Rad

iatio

n Ef

ficie

ncy

Frequency (Hz)


Figure 4.12 – Radiation efficiency for stainless-steel plate after particle velocity correction, 100-6000 Hz.

56

0.001

0.01

0.1

1

10

100 1000

Rad

iatio

n Ef

ficie

ncy

Frequency (Hz)

Accelerometer ArrayCorrected Particle Velocity

Figure 4.13 – Radiation efficiency for the gas tank after particle velocity correction, 125-5000 Hz.

57

CHAPTER 5 CONCLUSIONS AND FUTURE WORK

5.1 Conclusions

Acoustic radiation efficiency is defined as the radiated sound power divided by the

equivalent sound power from a baffled piston. It is well known that radiation efficiency

will approach or even exceed unity when the structural wavelength is on the same order

as or greater than the acoustic wavelength. The structural and acoustic wavelengths are

equal to one another at the coincidence frequency. This coincidence frequency can be

increased by reducing the thickness of a plate or more generally by reducing the stiffness.

In low stress components, the thickness can be reduced and low radiation efficiency can

be taken advantage of to reduce the emitted noise.

In the research reported in this thesis, a sound pressure - particle velocity combination

probe or PU probe is used to measure radiation efficiency. The suggested method appears

to be a promising alternative to ISO-7849 [25]. If ISO-7849 is used, the sound power is

measured using a sound intensity probe and the surface vibration is measured using

accelerometers. The PU probe permits direct and simultaneous measurement of sound

power and particle velocity at some distance from the vibrating surface. However, the

particle velocity will not be equal to the surface vibration because the particle velocity

decays with distance from the surface. Hence, it is best to measure close to the surface

and correct the result to better correlate with the surface vibration.

Test cases include a 3.175 mm thick aluminum plate, 1 mm thick stainless-steel plate, a

ribbed aluminum oil pan, and a two-shell composite gas tank. Based on these test cases, it

was established that the sound power could be accurately measured using the PU probe

and that the measured particle velocity could be corrected to correlate well with direct

measurement of surface vibration. It was shown that the most straightforward correction

was to measure acceleration on the surface and measure particle velocity at a set distance

away. The transfer function between the two measurements can be used as the correction.

By using the correction, it was shown that the radiation efficiency could be accurately

determined for each case.

58

5.2 Future Work

The current research paves the way for additional studies. These might include additional

validation of the measurement of radiation efficiency on other examples. The current test

cases were all plate-like structures. The approach should be further validated for a solid

component like an engine block.

Secondly, further work should be performed to establish a protocol for a scanning

measurement approach. This will likely include validating a correction approach and

selection of an optimal distance away from the source for measurement of particle

velocity. It is desirable to select a distance so that both sound power and the estimated

surface vibration can be determined with a single scan.

59

REFERENCES

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4. F. G. Leppington, E. G. Broadbent and K. H. Heron, “The Acoustic Radiation Efficiency of Rectangular Panels”, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 382(1783), 245-271, (1982).

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6. C. H. Hansen and D. A. Bies, “Near Field Determination of the Complex Radiation Efficiency and Acoustic Intensity Distribution for a Resonantly Vibrating Surface”, Journal of Sound and Vibration, 62(1), 93-110, (1979).

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11. M. Long, Architectural Acoustics, 2nd Edition, Academic Press, Waltham, MA, (2014).

12. Giancarlo Genta, Vibration Dynamics and Control, Springer, (2009).

13. Mark F. Jacobsen, Rajendra Singh and Fred B. Oswald, “Acoustic Radiation Efficiency Models of a Simple Gearbox”, (Army Research Laboratory Technical

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VITA

STEVEN CONNER CAMPBELL

PLACE OF BIRTH

Corbin, Kentucky EDUCATION

Eastern Kentucky University Bachelor of Science in Physics with Honors (July 2016)

PROFESSIONAL POSITIONS

Lockheed Martin (Production Engineer Planner) Lexington, Kentucky (September 2018-April 2019) University of Kentucky ME Dept. (Graduate Student/Research Engineer) Lexington, Kentucky (March 2017-September 2018) Briggs and Stratton (NVH Intern) Milwaukee, Wisconsin (May 2017- August 2017) Tribo Flow Separations (Research Engineer) Lexington, Kentucky (August 2016- March 2017) Aisin Automotive Casting Tennessee (Quality Engineer Intern) Clinton, Tennessee (June 2016- August 2016)

CONFERENCE PROCEEDINGS Steven Campbell, D. W. Herrin, Brett Birshbach, and Pat Crowley, “Notes on

Measurement of Radiation Efficiency”, Inter-Noise 2018 Conference, Chicago, Illinois, August 26-29, 2018.

D. W. Herrin, Gong Cheng, Steven C. Campbell, and J. M. Stencel, “Noise reduction on a jumbo drill using panel contribution analysis and scale modeling”, Inter-Noise 2017 Conference, Hong Kong, China, August 27-30, 2017.

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